A periodic Levinson-Durbin algorithm for entropy maximization
A recursive algorithm is presented for the computation of the first-order and second-order derivatives of the entropy of a periodic autoregressive process with respect to the autocovariances. It is an extension of the periodic Levinson-Durbin algorithm. The algorithm has been developed for use at one of the steps of an entropy maximization method developed by the authors. Numerical examples of entropy maximization by that method are given. An implementation of the algorithm is available as an R package.
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- Hindrayanto, Irma & Koopman, Siem Jan & Ooms, Marius, 2010. "Exact maximum likelihood estimation for non-stationary periodic time series models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2641-2654, November.
- Castro, Glaysar & Girardin, Valerie, 2002. "Maximum of entropy and extension of covariance matrices for periodically correlated and multivariate processes," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 37-52, August.
- Sophie Lambert-Lacroix, 2005. "Extension of Autocovariance Coefficients Sequence for Periodically Correlated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 423-435, 05.
- Georgi N. Boshnakov & Sophie Lambert-Lacroix, 2009. "Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(5), pages 467-486, 09.
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